bond valuation and risk ch-8

Financial Markets and Institutions6th Edition

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By Jeff Madura

CHAPTER

88Bond Valuation

and Risk

Copyright© 2002 Thomson Publishing. All rights reserved.

Chapter ObjectivesChapter Objectives

Demonstrate how bond market prices are established and influenced by interest rate movements

Identify the factors that affect bond prices Explain how the sensitivity of bond prices to

interest rates is dependent on particular bond characteristics

Explain the benefits of diversifying the bond portfolio internationally


Bond Valuation ProcessBond Valuation Process

Bonds are debt obligations with long-term maturities issued by governments or corporations to obtain long-term funds

Commonly purchased by financial institutions that wish to invest funds for long-term periods

Bond price (value) = present value of cash flows to be generated by the bond



Impact of the Discount Rate on Bond Valuation Discount rate = market-determined yield that

could be earned on alternative investments of similar risk and maturity

Bond prices vary inversely with changes in market interest rates Cash flows are contractual and remain the same each

period Bond prices vary to provide the new owner the market

rate of return


Bond Risks and PricesBond Risks and Prices

Higher risk Higher discount rates Lower bond prices

Lower risk Lower discount rates Higher bond prices

Note Inverse Relationship

Between Risk, required returns

and Bond Prices



Bond Price = present value of cash flows discounted at the market required rate of return C = Coupon per period (PMT) Par = Face or maturity value (FV) i = Discount rate (i) n = Compounding periods to maturity

PV = C

(1+ i)1+

(1+ i)2 (1+ i)nC C + Par+ …



Consider a $1000, 10% coupon (paid annually) bond that has three years remaining to maturity. Assume the prevailing annualized yield on other bonds with similar risk is 12 percent. Calculate the bond’s value. The expected cash flows of a coupon bond

includes periodic interest payments, and… A final $1000 payoff at maturity Discounted at the market rate of return of 12%



PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3

= $951.97

N I PV PMT FV

3 12 ? 100 1000



PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3

= $951.97

N I PV PMT FV

3 12 –951.97 100 1000



Valuation of Bonds with Semiannual Payments Most bonds pay interest semiannually Double the number of compounding periods (N)

and halve the annual coupon amount (PMT) and the discount rate (I)


Re-work the above problem assuming semiannual compounding

N I PV PMT FV

6 6 ? 50 1000


Re-work the above problem assuming semiannual compounding

N I PV PMT FV

6 6 950.82 50 1000


Relationships Between Coupon Rate, Relationships Between Coupon Rate, Required Return, and Bond PriceRequired Return, and Bond Price

No periodic coupon Pays face value at maturity Trade at discount from face value No reinvestment risk Considerable price risk

Zero-Coupon Bonds



Discount bonds are bonds priced below face value; premium bonds above face value

Discounted bond Coupon < Market rates Rates have increased since issuance Adverse risks factors that may have occurred

Price risk—depends on maturity Default risk may have increased Fisher effect of higher expected inflation



Premium bond Coupon > Market Rates decreased since issuance Favorable risk experience

Price risk—depends on maturity Default risk might have decreased as economic activity

has increased Low inflation expectations



Long-term bond prices are more sensitive to given changes in market rates than short-term bonds

Changes in rates compounded many times for later coupon and maturity value, impacting price (PV) significantly

Short-term securities have smaller price movements

Bond Maturity and Price Variability


Exhibit 8.4Exhibit 8.4

0 5 8 10 12 15 200

1,800

1,600

1,400

1,200

1,000

800

600

400

200

5-Year Bond10-Year Bond20-Year Bond

Required Return (Percent)



Low coupon bond prices more sensitive to change in interest rates

PV of face value at maturity a major proportion of the price

Coupon Rates and Price Variability


Explaining Bond Price MovementsExplaining Bond Price Movements

The price of a bond should reflect the present value of future cash flows discounted at a required rate of return

The required return on a bond is primarily determined by Prevailing risk-free rate Risk premium



Factors that affect the risk-free rate Changes in returns on real investment

Financial investment an alternative to real investment Opportunity cost of financial investment is the returns

available from real investment Federal Government deficits/surplus position

Inflationary expectations Consumer price index Federal Reserve monetary policy position Oil prices and other commodity prices Exchange rate movements



Factors that affect the credit or default risk premium Strong economic growth

High level of cash flows Investors bid up bond prices; lower default premium

Weak economic growth Lower profits and cash flows Impact on specific industries varied Investors flee from risky bonds to Treasury bonds Bond prices fall; default premiums increase


Exhibit 8.8Exhibit 8.8

U.S.FiscalPolicy

U.S.Monetary

Policy

Long-TermRisk-Free

Interest Rate(TreasuryBond Rate)

RiskPremiumof Issuer

U.S.Economic

Conditions

Issuer’sIndustry

Conditions

Issuer’sUnique

Conditions

RequiredReturnon theBond

Bond Price


Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements

Bond Price Elasticity = Bond price sensitivity for any % change in market interest rates

Bond Price Elasticity = (% Change In Price)/(% Change In Interest Rates)

Increased elasticity means greater price risk



Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. First, calculate the price of the bond for both rates

When k = 10%, PV = ? When k = 8%, PV = ? Hint: Remember zero-coupon or no PMT in this

calculation The price of a zero-coupon bond is the present value of

a single future value cash flow.



Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. First, calculate the price of the bond for both rates

When k = 10%, PV = $386 When k = 8%, PV = $463



Calculate the bond elasticity:

997.

%10%10%8

386$386$463$

kpercent

PpercentPe

Bond elasticity or price sensitivity to changes in interest rates approaches the limit at –1 for zero-coupon

bonds. Price sensitivity is lower for couponbonds. The inverse relationship between k and p

causes the negative numbers



Price-Sensitive Bonds Longer maturity—more price variation for a

change in interest rates Lower coupon rate bonds are more price sensitive

(the PV is a greater % of current value) Zero-coupon bonds most sensitive, approaching –

1 price elasticity Greater for declining rates than for increasing

rates



Measure of bond price sensitivity Measures the life of bond on a PV basis Duration = Sum of discounted, time-weighted cash

flows divided by price

Duration



The longer a bond’s duration, the greater its sensitivity to interest rate changes

The duration of a zero-coupon bond = bond’s term to maturity

The duration of any coupon bond is always less than the bond’s term to maturity

Duration



Modified duration is an easily calculated approximate of the duration measure

)1(*

k

DURDUR

DUR* is a linear approximation of DUR which measuresthe convex relationship between bond yields and prices


Bond Investment Strategies Used by Bond Investment Strategies Used by InvestorsInvestors

Create bond portfolio that will generate income that will match their expected periodic expenses

Used to provide retirement income from savings accumulation

Estimate cash flow needs then select bond portfolio that will generate needed income

Matching Strategy



Funds are allocated evenly to bonds in several different maturity classes

Example: ¼ funds invested in bonds with 5 years until maturity, ¼ in10-year bonds, ¼ in 15-year bonds, and ¼ in 20-year bonds

Investor receives average return of yield curve over time as maturing bonds are reinvested

Laddered Strategy



Allocated funds to short-term bonds and long-term bonds

Short-term bonds provide liquidity from maturity Long-term bonds provide higher yield (assuming

up-sloping yield curve)

Barbell Strategy



Funds are allocated in a manner that capitalizes on interest rate forecasts

Example: if rates are expected to decline, move into longer-term bonds

Problems: High transaction costs because of higher trading Difficulty in forecasting interest rates

Interest Rate Strategy


Foreign Exchange Rates and Interest Foreign Exchange Rates and Interest RatesRates

Country interest rate differences reflect expected future spot foreign exchange rates

Expected future spot foreign exchange rates (forward forex rates) reflect expected inflation differences between countries

Expected return on foreign bond portfolio related to return on bonds adjusted for expected changes in forex rates


Diversifying Bonds InternationallyDiversifying Bonds Internationally

Investor may diversify by: Credit risk Country risk Foreign exchange risk Interest rate risk

Seek lower total variability of returns per level of risk assumed

bond valuation and risk ch-8

Documents

interest rate

bond valuation

bond investment

maturity default

interest rates

market rate

term bonds

coupon rate